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MTH101 ASSIGNMENT 1 SOLUTION FALL 2021
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Question:
Consider the equation of a circle x2-2x+y2-4y-4=0. If the line 2x-y+a=0 is its diameter. Then find the value of a.
Solution:
x²-2x+y²-4y-4=0 …… (1)
General Form is
x²+y²+2gx+2fy+c=0 ……. (2)
Comparing eq 1 and 2
2g=-2
g=-1
2f=-4
f=-2
We know that
Center (-g, -f)
C (1, 2)
Diameter lines pass through the point to the center of the circle, So the center point is satisfying the line.
2x-y+a=0
2(1)-(2) +a=0
2-2+a=0
-2+a= -2
a = -2+2
a=0
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